Measuring the harmonic content would involve using what is called a spectrum analyzer. It performs a FFT across the frequency spectrum and would key you in on what the harmonic output of your 60Hz waveform was.
Then would come the hard part: If you're lucky, pull up a datasheet on a 5/6th pitch generator and it will let you know how much attenuation there is for the 3rd, 5th, 7th.. etc harmonic. Compare to the results you get on your spectrum analyzer.
I think that the better approach involved looking at the windings of the generator if you can, as Wolf mentioned. I don't know how difficult this might be based on actually being able to get to this area of the generator and make sense of it.
The BEST option, of course, is to get the nameplate information, and then find the manufacturer's datasheet information on what the pitch is.